Select the expressions that are equivalent to 3(7q+8)+5.

Question

1) 36z+24
2) 3(9+6z)+3(3+2z)
3) 12z+36
4) 24z+36

Answer 1

To determine which expressions are equivalent to \( 3(7q+8)+5 \), we will first simplify this expression.

1. Start with the original expression: \[ 3(7q + 8) + 5 \]

2. Distribute \( 3 \): \[ 3 \cdot 7q + 3 \cdot 8 + 5 = 21q + 24 + 5 \]

3. Combine like terms: \[ 21q + 29 \]

Now we will evaluate each option to see if it simplifies to \( 21q + 29 \).

Option 1: \( 36z + 24 \)

• This expression does not contain \( q \). Therefore, it cannot be equivalent to \( 21q + 29 \).

Option 2: \( 3(9 + 6z) + 3(3 + 2z) \)

• First, let's simplify this: \[ 3(9 + 6z) = 27 + 18z \] \[ 3(3 + 2z) = 9 + 6z \] Now combine both results: \[ 27 + 18z + 9 + 6z = 36 + 24z \]
• This also does not contain \( q \), hence it cannot be equivalent to \( 21q + 29 \).

Option 3: \( 12z + 36 \)

• This expression does not contain \( q \) either, so it cannot be equivalent to \( 21q + 29 \).

Option 4: \( 24z + 36 \)

• Similar to previous options, this expression does not contain \( q \), so it cannot be equivalent to \( 21q + 29 \).

After analyzing all options, none of the provided expressions are equivalent to \( 3(7q + 8) + 5 \). Thus, the answer is that none of the options provided are equivalent to \( 21q + 29 \).